Problem
A prime is an integer greater than 1 with no positive divisors other than 1 and itself. Find the largest prime factor of n. When n is itself prime, return n.
Implement largest_prime_factor(n).
Input
n: The integer to factor.
Output
Return its largest prime divisor.
Constraints
2 ≤ n ≤ 10¹². The input 1 is excluded because it has no prime factor.
Examples
Input:
n = 84
Expected output:
expected = 7Input:
long long n = 84;
Expected output:
long long expected = 7;Input:
long n = 84;
Expected output:
long expected = 7;Explanation
84 = 2 × 2 × 3 × 7, so the largest prime factor is 7.
Input:
n = 13
Expected output:
expected = 13Input:
long long n = 13;
Expected output:
long long expected = 13;Input:
long n = 13;
Expected output:
long expected = 13;Explanation
13 is prime, so it is its own largest prime factor.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Remove small prime factors first; any remaining value can only shrink, and the last factor left is the answer.
Hint 2
Test divisors only up to the square root of the current remainder, and divide it out repeatedly when it fits.
Hint 3
If the remainder is still above 1 after checking smaller factors, that remainder is prime and is the largest factor.
Expected complexity
O(√n) time, O(1) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.